Gravimeter



Jan. 11, 1955 R. K. A. TOMASCHEK 1 2,699,067

' GRAVIMETER Filed May 10, 1950 v 8 Sheets-Sheet l 7O 8O 90 I00 I10 I I I I Rudolf Karl Anton Tomaschek Jan. 11, 1955 R. K. A. TOMASCHEK 2,699,067

GRAVIMETER Filed May 10, 1-950 v 8 Sheets-Sheet 2 QQQQ o2 om QQQQ 0Q 0% ON Inventor: Rudolf Karl Anton Tomaschek B 1 aa zmi y A tornevsk Jan. 11, 1955 R. K. A. TIOMASCHEK 2,699,067

' GRAVIMETER 7 Filed Ma 10, 1950 s Shets-Sheeq 5 Inventor:

Ruflolf Kar'l Anton .Tona sch ek R. K. A. TOMASCHEK Jan. 11, 1955 GRAVIMETER 8 Sheets-Sheet 6 Filed May 10 1950 Inventor:

Rudolf Karl Anton Tomaschek yk wf Attornevs.

1955 R. K. A. TOMASCHEK 2,699,067

' r V GRAVIMETER Filed May 10, 1950 8 Sheets-Sheet '7 Inventor:

Rudolf Karl Anton Tomaschek M. a m 1 M Attorneys.

Jan. 11, 1955 R. K. A. TOMASCHEK 2,699,067

GRAVIMETER Filed May 10, 1950 s Sheets-Sheet s Inventor:

Rudolf Karl Anton Tomaschek AttornevL United States Patent GRAVIMETER Rudolf Karl Anton Tomaschek, London, England, as-

signor to Anglo-Iranian Oil Company, Limited, London, England, a British joint-stock corporation Application May 10, 1950, Serial No. 161,167

Claims priority, application Great Britain May 11, 1949 8 Claims. (Ql. 73-382) The invention relates to gravimeters.

The term gravimeter is employed in its widest sense to include any instrument for measuring, indicating, recording, comparing or relaying a function of the force of gravity at a given location.

Conventional gravimeters comprise a fine spring which is distorted under the influence of gravity upon a mass attached to the spring. In general, a substantially linear relationship exists between stress and strain from zero loading over a range of loadings characteristic of the spring.

It has now been found that if a curved spring, such as a coiled spring of diminishing radius of curvature towards one end thereof is rigidly fixed at one end and a force applied to the free end of the spring in a direction at a small angle to the axis of the spring, for the purpose of distorting the spring, there exist under certain conditions of magnitude and direction of the applied force, as hereinafter described, one or more zones of high sensitivity which are of particular value when employed as the operating range in a measuring, indicating, recording or relaying instrument of which the spring forms part.

It is an object of the invention to provide an improved gravimeter of high sensitivity.

According to the invention there is provided a gravimeter comprising a coiled spring of material having a cross-section of substantial width/thickness ratio, and constituting not substantially less than 1.25 turns in the unextended state, means attached or attachable to one end of the spring capable of movement under the action of the force of gravity, and a mounting for the other end of the spring to support, or adapted to support the spring so that the longitudinal axis, in the unextended state subtends a small angle to the vertical, the angle being such that under the influence of the force the spring is extended into a state of extreme sensitivityas hereinafter described.

According to a modification of the form of construction of the graviineter, the instrument comprises a coiled spring of material having a cross-section of substantial width/thickness ratio, and constituting not substantially less than 1.25 turns in the unextended state, means attached or attachable to one end of the spring capable of movement under the action of the force of gravity and a mounting for the other end of the spring to support, or adapted to support the spring so that the longitudinal axis of the spring, in the unextended state subtends a small angle to the horizontal, the angle being such that, under the influence of the force the spring is extended into a state of extreme sensitivity as hereinafter described.

Preferably the angle subtended by the axis of the unextended spring to the direction of the linearforce is not less than and in most cases satisfactory performance is obtained when the angle lies in the range 10-40. The ratio of the width/thickness of the spring is preferably in the range 10-100. If the ratio exceeds 100 in most cases the windings will touch during extension, thereby interfering with the correct performance of the spring. The spring used according to the invention may be of any metal or alloy conventionally employed in the construction of springs, for example, steel, Invar and beryllium-copper alloys.

Preferably, the coiled spring in the undistorted state approximates to a circular form. Alternatively, the spring may take the form of other curved shapes, for ex- "ice ample, elliptical, parabolic or hyperbolic or combinations of these or other shapes.

The measurement of the distortion produced in the spring under the action of gravity may be made with reference to the linear distortion of the spring, for example, by observation with a travelling microscope, or by eifecting variations in the capacity of a variable condenser; alternatively measurement of the distortion produced in the spring may be made with reference to the angular displacement of the free end of the spring, for example, by measuring the displacement of a beam of light reflected in a mirror attached to the spring.

If desired electrical contacts may be provided whereby an electrical circuit is closed by the spring on extension to a given length or on rotation, at the free end through a given angle. be operated in response to the closing of the circuit.

Preferably a conventional helical spring is attached by one end to the free end of the sensitive spring or is in rigid connection therewith, the other end of the helical spring being restrained but being capable of adjustment in the vertical direction, for example, by operation of a rack and pinion.

The mounting for the supported end of the sensitive spring is preferably angularly adjustable in a vertical plane. More particularly it is preferred that the mounting be angularly adjustable in two mutually perpendicular vertical planes.

The determination of the zone of extreme sensitivity is illustrated with reference to the accompanying Figures 1 to 7 of the accompanying drawings in which:

Figure 1 is a plan view of a coiled spring in the unextended state.

Figure 2 is an elevation of the same spring in the extended state.

Figures 3 to 7 are graphs indicating the relation of variable functions including angle or mounting, load and sensitivity.

Figures 8 and 9 show plots as determined for another sprmg.

Figures 10-15 illustrate a gravimeter according to the present invention.

The coiled spring employed (Figs. 1-7) had the following dimensions.

Free of distorting forces the spring had 3% windings and the outer end was approximately 15 mm. from the centre of the geometric form.

The spring 1 was clamped at its inner end in a substantially horizontal plane and extended by attaching a mass to its free end.

At the outer end of the spiral spring a scale was attached by means of a ring. The sinking of the scale was measured by means of a mirror rule. The horizontal projection of the twist of the outer end of the spiral spring was measured by the twist of the scale. An arrow was secured to the scale to extend horizontally. A small source of light projected the shadow of the arrow on to a sheet of paper disposed in a horizontal plane. The two end points of the arrow were marked and later connected by a straight line. The lower end of the spiral spring was left free and in this way the influence of lateral shifting on the reading of the angles was avoided.

Figure 3 is a plot of the extension of the spring (h) in mm./ applied load (g) in grams.

Figure 4 is a plot of the angular disposition of the free end of the spring (oc)/ applied load in grams.

It will be seen from Figures 3 and 4 that considerable deviations from a linear relationship exist and that at certain loadings the slope of the curve is very steep indicating increased sensitivity.

Figure 5 is a plot of the sensitivity for twist e=Aoc/ Ag) applied load in grams.

Regions of high sensitivity about 51 grams and grams.

The spring was then tilted by adjustment of the mountare noted at loadings of By the use of relays other apparatus may 3 ing so that the restrained end of the spring made a small angle (1/1) with the horizontal. The convention adopted is an initially upward inclination of the spring, 0: an initially downward inclination of the spring.

Figure 6 is a plot, at different positive values of 11/, of the angular disposition of the free end of the spring (a) applied load in grams.

Assuming, for example a value of =+30, on increasing the load g the curve A'B is traversed. At B the spring extends suddenly, the free end lengthening and twisting considerably for a very small increase in load until the position represented by C is reached. Further loading produced a more gradual extension and twist, following the curve C-C'.

On reducing the loading, the spring does not contract violently at C but continues to follow an extension of the curve C'-C to the point D when a sudden contraction and twist for a small decrease in loading brings the spring to the conditions represented by A. Further re duction in loading follows the course AA.

For the spring employed it was found that on reducing the angle #1 similar curves were obtained on plotting a/ g until a value between v,!/=j-7.5 and b -j-S was reached when the abnormal behaviour of the spring disappeared and simple inflection curves were obtained.

The critical angle (rim) is defined as the value or values of l/(+ive or ive) at which the points A and B coincide.

The critical loading (gcr) is defined as the value of g at the point A at the critical angle.

If the spring has a number of turns the conditions illustrated on Figure 6 may recur at higher values of g.

Thus a spring may have a plurality of values of I/lcr both positive and negative.

The spring is defined as being in a state of extreme sensitivity when it is mounted at an angle approximately to gbcr under a critical loading (gcr) corresponding to 111m.

The spring described with reference to Figure 1 has been found to possess two primary states of extreme sensitivity.

(l) at cr:+6 under load of approximately 51 grams. (2) at 3//cr=19 under load of approximately 77 grams.

Secondary and tertiary states of extreme sensitivity are probable at higher values of g.

Figure 6 as described above illustrates the behaviour of the spring with reference to angle of twist (on). It is to be noted, however, that the relationship between a and h for different values of 1 is very nearly linear above and below the zones of instability between the position A and B, C and D.

Figure 7 is a plot of a/h at different values of 4/. Measurement or indication of small changes in the value of g when operating in the state of extreme sensitivity may thus be made with respect to changes in length or in angle of twist.

Figures 8 to 9 show plots of the variables hereinbefore described as determined for another spring of the type illustrated in Figure 1 and Figure 2 and having the following dimensions:

Free of distorting forces the spring had 3% windings.

The outer end was approximately 27 mm. from the centre of the geometric form.

The spring was clamped at its inner end and mounted to permit inclination of the end of the spring while niaintaining the longer side of the spring in a vertical p ane.

fFigure 8 is a plot of Ot/ applied load at different values o ,0.

A region of high sensitivity is noted at a value of 1//:-|17 and a loading of approximately 238 grams.

Figure 9 is a plot of x/// at for six different values of the load, approximating to the critical loading, between 236 and 239 grams.

It is noted that at a value of approximately 238 grams, the distortion is substantially independent of the angle of application of the loading between values of 13 and 17. Similar curves are obtained when tilting the clamped) end in a direction which is at right angles to 1/ (i. e. 5

In general it is preferred that an instrument according to the present invention be operated under a load such that the distortion is nearly independent as possible of the angle of loading (,0 and for small variations of b and Under these conditions the effect of errors or variations in the levelling of the instrument are minimised.

One form of construction of a gravimeter according to the present invention will be described in detail as illustrated in Figures 10 to 15 of the accompanying drawings.

A rigid rectilinear framework 1 has an adjustable spring mounting clamp 2 attached to the lower side of its upper surface, and to the movable part of the mounting clamp is rigidly clamped the inner end of the coiled flat section spring 3. The spring, free of distorting forces, comprises approximately three complete turns. To the outer end of the spring, which under the influence of the masses attached thereto depends below the upper fixed end, there is attached a small mirror 4 and to the mirror one end of a light vertical rod 5. The lower end of the rod is attached to the upper end of a vertical, delicate, helical spring 6, the lower end of the helical spring being attached to a vertical rack 7, carried by a slide rigidly secured to the framework 1 and engaging a pinion 9 operated by a horizontal shaft 10 projecting through one side of the framework 1. Within the spring 3 there is extended a vertical delicate, helical spring 8 attached at its upper end to the mounting clamp 2 and at its lower end to the mirror 4. The vertical rod 5 carries a horizontal double-bladed vane 11 which moves between quadrants 12 disposed as in a quadrant electrometer, that is, comprising two diagonally opposed quadrants in a plane above the vane and two diagonally opposed quadrants situated below the vane, preferably two adjacent quadrants, that is one quadrant above the vane and one below. The vane is attached to a movable support 13 and may be adjusted in a vertical direction between their corresponding rigidly held quadrants. A horizontal damping disc 14 is mounted on the vertical rod 5 near its lower end, having its periphery between the pairs of poles 15 of two diametrically positioned horse-shoe magnets rigidly attached to the framework or box. Preferably the vane, quadrants and disc are constructed of a light metal, such as aluminum. Preferably clamps are provided to lock the vertical rod against horizontal movement and the disc against vertical movement when the apparatus is not in use.

Pairs of quadrants are connected to an electronic circuit by which readings are made of the force of gravity after calibration of the instrument. A variable capacity condenser of this type is very sensitive and permits accurate measurement of the force of gravity.

Alternatively a photo-electric method can be employed using a beam of light reflected by the small mirror attached at the head of the vertical rod.

Alternatively a radio active method using a source of radio active material which changes the ionisation within two or more ionisation chambers, the chambers and the source being capable of relative movement.

By adjustment of the vertical movable quadrants a position can be reached in which the instrument is selfcompensating for small angles of tilt.

The adjustable mounting for the sensitive spring may be constructed in numerous ways, and the form of construction employed is not an essential feature of the invention.

Figures 11 and 12 illustrate one form of spring mounting for use in a gravimeter according to the invention. Figure 11 is an elevated view and Figure 12 a plan of the apparatus.

The sensitive spring 20 is clamped on to support 21 carried by bevel gear 22 mounted on a cranked arm 23 supported by the casing 19. A second bevel gear 24 engages gear 22 and is carried on a shaft 25 within one arm of 23, adjusting wheels 26 and 27 are carried by the arm 23 and shaft 25 to enable the spring 20 to be tilted in two directions mutually at right angles.

Figures 13 and 14 illustrate a second form of spring mounting. Figure 14 is an elevated view and Figure 13 is a plan.

The spring 30 is clamped on to support 31 attached to a ball socket 32 carrying four vanes, 33-36. The socket 32 encloses a spherical ball 37 rigidly supported by a rod 38 from the casing 39. Two adjacent vanes 33 and 34 are 5 supported from the casing 39 by spring loaded rods 40 and 41. The other two vanes 35 and 36 are adjustably positioned by adjusting screws 42 and 43 which are threaded through the casing 39.

In general it is preferred that an instrument according to the present invention be operated under a load such that the distortion is virtually independent of the angle of loading (\p) for small variations of 1/. Under these conditions the effect of errors or variations in the levelling of the instrument are minimised.

The following general laws enable the determination of the value of unknown factors when certain characteristics of the spring are known.

Law 1.For constructing a sensitive spring for a given weight the following approximative formula (il%) may be used.

E.h.b

where E=modulus of elasticity h=width of the spring b=thickness of the spring d=length of the sensitive part of the spring Taking a spiral spring of 1 /2 turns in the initial shape and using inclinations, d can be taken as approximately equal to half of the circumference of the first turning (at the clamped end) of the spiral. When using negative inclinations W- is approximately equal to l.5W+. For 0 inclination W-=1.25 W+. The shape factor a is supposed to have the value of between 0.03 and 0.9. This factor is defined by R,,= R,- nXR, where Ri=radius at the inner, clamped end, Ra=radius at the outer end, n=number of windings.

The values obtained are also valid for springs with 3 /2 windings, but the absolute value of the angles or will be diiferent.

The following examples illustrate the calculation of the value of W when other characteristics of the spring are known.

W calc.: 6 gr. W obs.: 6.6 gr. for-l-incl. 5 W ealc.: 9 gr. W obs.: 10.6 gr. tor-incl. W calc.: 7.0 gr. W obs.: 7.1 gr. for-41 incl.

EXAMPLE 2 Using a spring having the same characteristics as in Example 1 except that the value of b=0.008 in. the following theoretical and practical results were obtained:

W calc.: 25 gr. W obs.: 23.0 gr. tor+incl. 4:

W ealc.: 37 gr. W obs.: 35.5 gr. ion-incl. W 02110.: 28.5 gr. W obs.: 27.5 gr. tor-p incl.

Law 2.As the diameter of the spiral increases with so (the overall length) if the shape remains similar (1,!/=const.) W is also proportional to l/so in this case.

Law 3.-Another dimension which one wishes to be able to calculate beforehand is the vertical length 1cr of the spring in its sensitive state compared with the overall length so. The ratio =I =relative working length) is given in the following table:

I values P -\l' T111118 The ratio of I W to 131/2 is for every shape 1.6.

It is apparent that inclination gives the shortest and -1// inclination the longest relative working length.

Law 4.--The ratio between lengthening and twisting of the spring. (K mm./degree) is a linear function of so and therefore also of lcr. According to the figures given in the section above K is lowest for and increase for and then for For 1 /2 turns and so=150 mm. K is in the order of magnitude of 0.3 mm./degree for and increases to 0.6 for so of about 400 mm.

For the same value of lor the value of K is substantially lower for 3 /2 turns than for 1 /2 turns.

The invention is further illustrated but in no way limited with reference to the following examples.

EXAMPLE 3 A steel clock of width (h) 0.755 inch, breadth (b) 0.008 inch, h/b ratio of 94 and comprising 1 /2 turns was investigated to determine its states of extreme sensitivity. These were found to occur under the conditions shown in the following table.

Angle of inclination, W. (grams) 1 Moms.)

degrees EXAMPLE 4 A steel clock spring of width (h) 0.755 inch, breadth (b) 0.008 inch, h/b ratio of 94 and comprising 3 /2 turns was investigated to determine its states of extreme sensitivity. These were found to occur under the conditions shown in the following table.

Angle of inclination, W. (grams) 1"(cms.)

degrees It is frequently advantageous that the action of the sensitive spring should be modified by the use of a subsidiary helical spring of conventional type connected in parallel. The subsidiary spring should be very weak in comparison with the sensitive spring and its action is to restrict the movement of the sensitive spring outside the operating range of movement and to stabilise the action of the sensitive spring.

In order to attain conditions under which the elfect of variations of the angle of levelling are minimised, it is advisable to suspend the working part of the gravimeter within a fluid in a sealed vessel, so that the working part maintains, automatically, its vertical position.

I claim:

1. A sensitive gravimeter comprising a coiled spring and a comparatively weak helical spring, said coiled spring being of diminishing radius of curvature towards one end thereof of material having a cross-section of width/thickness ratio in the range 10:1 to 100:1 and constituting not substantially less than 1.25 turns in the unextended state, means attached to one end of the coiled spring capable of movement under the action of the force of gravity, and a mounting for the other end of the coiled spring to support said spring so that the longitudinal axis, in the unextended state subtends an angle in the range of from 5 to to the vertical, the angle being such that under the influence of the force of gravity the coiled spring is extended into a state of extreme sensitivity, the action of the coiled spring being modified by said comparatively weak helical spring, rigidly connected to the coiled spring at each end thereof.

2. A sensitive gravimeter as specified in claim 1 in which in the operating position the angle of inclination of the axis of the coiled spring to the vertical is in the range 10-40".

3. A sensitive gravimeter comprising a coiled spring of diminishing radius of curvature towards one end there- 88 of of material having a cross-section of width/thickness ratio in the range 10:1 to 100:1 and constituting not substantially less than 1.25 turns in the unextended state, means attached to one end of the spring capable of movement under the action of the force of gravity, and a mounting for the other end of the spring to support the spring so that the longitudinal axis, in the unextended state subtends an angle in the range of from 5 to 85 to the vertical, the angle being such that under the infiuence of the force the spring is extended into a state of extreme sensitivity, in which the end of the spring capable of movement under gravity is connected to a quadrant electrometer.

4. A sensitive gravimeter as specified in claim 3 in which in the operating position the angle of inclination of the axis of the spring to the vertical is in the range 10-40.

5. A sensitive gravimeter as specified in claim 3 in which the end of the spring capable of movement under gravity is connected to a movement damping device.

6. A sensitive gravimeter comprising a coiled spring of diminishing radius of curvature towards end thereof of material having a cross-section of width/thickness ratio, in the range of 10:1 to 100:1 and constituting not substantially less than 1.25 turns in the unextended state, means attached to one end of the spring capable of movement under the action of the force of gravity, and a mounting for the other end of the spring to support the spring so that the longitudinal axis, in the unextended state subtends an angle in the range of from 5 to 85 to the vertical, the angle being such that under the influence of the force the spring is extended into a state of extreme sensitivity, and in which the end of the coiled spring capable of movement under gravity is connected to one end of a vertical helical spring, the other end of said 8 helical spring being attached to a vertically adjustable mounting.

7. A sensitive gravimeter as specified in claim 6 in which in the operating position the angle of inclination of the axis of the spring to the vertical is in the range 10 0.

8. A sensitive gravimeter comprising a coiled spring of diminishing radius of curvature towards one end thereof of material having a cross-section of width/thickness ratio in the range 10:1 to 100:1 and constituting not substantially less than 1.25 turns in the unextended state, means attached to one end of the spring capable of movement under the action of the force of gravity, and a mounting for the other end of the spring to support the spring so that the longitudinal axis, in the unextended state subtends an angle in the range of from 5 to 85 to the vertical, the ,angle being such that under the infiuence of the force the spring is extended into a state of extreme sensitivity, in which the action of the coiled spring is modified by a comparatively weak helical spring rigidly connected to the sensitive spring at each end thereof and in which the end of the sensitive spring capable of movement under gravity is connected to one end of a vertical helical spring, the other end of said vertical helical spring being attached to a vertically adjustable mounting.

References Cited in the file of this patent UNITED STATES PATENTS 2,087,354 Mufily July 20, 1937 2,131,738 Holt Oct. 4, 1938 2,131,739 Holt Oct. 4, 1938 2,293,437 La Coste Aug. 18, 1942 

